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FastOpt
Quantitative Design of
Observational Networks
M. Scholze,
R. Giering, T. Kaminski, E. Koffi
P. Rayner, and M. Voßbeck
Future GHG observation WS, Edinburgh, Jan 2008
FastOpt
Motivation
Can construct a machinery that, for a given network and a given target quantity, can approximate the uncertainty with which the value of the target quantity is constrained by the observations
What is the question?
FastOpt
Outline
• Motivation
• Example
• Method
• Demo
• Which assumptions?
• Links to further information
• Discussion -> Potential application or UK GHG monitoring strategy, CCnet proposal?
FastOpt
Example Linear Model
• From Rayner et al. (Tellus, 1996)
• Inverse model based on atmospheric tracer model
• Extend given atmospheric network CO2
• Target quantity: Global Ocean uptake
Figure shows additional station locations for two experiments, “1” additional site allowed / “3” additional sites allows
FastOpt
Posterior Uncertainty
If the model was linear:
and data + priors have Gaussian PDF, then the posterior PDF is also Gaussian:
with mean value:
and uncertainty:
which are related to the Hessian of the cost function:
For a non-linear model, this is an approximation
-
FastOpt
Model and Observational Uncertainties No observation/no model is perfect.
It is convenient to quantify observations and their model counterpart by probability density functions PDFs.
The simplest assumption is that they are Gaussian.
If the observation refers to a point in space and time, there is a representation error because the counterpart simulated by the model refers to a box in space and time.
The corresponding uncertainty must be accounted for either by the observational or by the model contribution to total uncertainty.
total uncertainty uncertainty from model error
uncertainty from observational error
FastOpt
Carbon Cycle Data Assimilation System (CCDAS) Forward Modelling Chain
Process Parameters
BETHY + background fluxes
TM2 LMDZ
Surface Fluxes
CO2 Flask CO2 continuous eddy flux
FastOpt
Sketch of Network Designer
Observations [sigma]
+ Flask [enter]x Continuous [enter]o Eddy Flux [enter]
|Compute|
Targets [sigma]
European Uptake [ ]Global Uptake [ ]
FastOpt
Assumptions and Ingredients
Assumptions:
• Gaussian uncertainties on priors, observations, and from model error (or function of Gaussian, e.g. lognormal)
• Model not too non linear
• What else?
Ingredients
• Ability to estimate uncertainties for priors, observations and due to model error
• Assimilation system that can (efficiently) propagate uncertainties (helpful: adjoint, Hessian, and Jacobian codes)